Ray-Bundle-Based X-Ray Representation and Reconstruction: An Alternative to Classic Tomography on Voxelized Volumes

Tomography recovers internal volume from projection measurements. Formulated as inverse problems, classic computed tomography generally reconstructs attenuation property in a preset cartesian grid coordinate. While this is intuitive and convenient for digital display, such discretization leads to forward-backward projection inconsistency, and discrepancy between digital and effective resolution. We take a different perspective by considering the image volume as continuous and modelling forward projection as a hybrid continuous-to-discrete mapping from volume to detector elements, which we call "ray bundles". The ray bundle can be regarded as an unconventional heterogenous coordinate. Projections are modeled as line integrations along ray bundles in the continuous volume space and approximated by numerical integration using customized sample points. This modeling approach is conveniently supported with an implicit neural representation approach. By representing the volume as a function mapping spatial coordinates to attenuation properties and leveraging ray bundle projection, this approach reflects transmission physics and eliminates the need for explicit interpolation, intersection calculations, or matrix inversions. A novel sampling strategy is further developed to adaptively distribute points along the ray bundles, emphasizing high gradient regions to allocate computational resources to heterogenous structures and details. We call this system T-ReX to indicate Transmission Ray bundles for X-ray geometry. We validate T-ReX through comprehensive experiments across three scenarios: simulated full-fan projections with primary signal only, half-fan setups with simulated scatter and noise, and an in-house dataset with realistic acquisition conditions. These results highlight the effectiveness of T-ReX in sparse view X-ray tomography.